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Analytic approximation to delayed convection dominated systems through transforms

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Abstract

In this paper we consider a family of singularly perturbed delay differential equation of convection diffusion type. When the perturbation parameter is very small, the solution of the problem exhibits layer behavior. In the layer region the solution changes rapidly, while away from this region the change in the solution is moderate. This simultaneous presence of two different scales phenomena makes the problem stiff. In this work, the problem is solved by applying a new Liouville–Green transform and the asymptotic solutions are obtained. Application to multi-point boundary value problem is also illustrated. Several test examples are taken into account so as to test the efficiency of the proposed method. The method presented is compared with other existing numerical or asymptotic methods. It is observed that the method presented is very easy to implement and is capable of reducing the size of calculations significantly while still maintaining high accuracy of the solution.

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Authors and Affiliations

  1. University Institute of Engineering and Technology, Panjab University, Chandigarh, 160014, UT, India

    Aditya Kaushik

  2. Department of Mathematics, KVA DAV College, Karnal, 132001, Haryana, India

    Manju Sharma

  3. Department of Mathematics, Honghe University, Mengzi, 661100, Yunnan, People’s Republic of China

    Chenglin Li

Authors
  1. Manju Sharma
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  2. Aditya Kaushik
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  3. Chenglin Li
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Corresponding author

Correspondence to Aditya Kaushik.

Additional information

The author greatfully acknowledges financial support from University Grants Commission (New Delhi, India) under Start-up Grant F.20-30(12)/2012(BSR).

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Sharma, M., Kaushik, A. & Li, C. Analytic approximation to delayed convection dominated systems through transforms. J Math Chem 52, 2459–2474 (2014). https://doi.org/10.1007/s10910-014-0394-1

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  • DOI: https://doi.org/10.1007/s10910-014-0394-1

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